LGA is definately do-able, but JFK might be better. I would say you might want to consider which airport you'll be commuting to most. I rarley have trouble getting in to JFK because there are plenty of flights so my pad is closer to Kennedy. If you have limited options into JFK but much better prospects into LGA then that might be easier.
Either way though, both could work.
The car service that most use (Kew Car Service) is about $20.00 (with tip) between the 2 airports and about $15.00 (with tip) between the crash pad area and either airport.
Last night I got from JFK to LGA in about 15-20 mins with no traffic. Can obviously be considerably more if traffic is heavy.
The bus is the cheaper alternative from crash pad to airport at $2.00, but I find it to be a pain in the a$$.